It is a common misconception that using a motorhome is cheaper than flying, or even staying in a hotel.
Trust me, when you check the rates at the various motor home rental agencies, it's not. Cruise America, for example, charges $900 for 10 days, plus a fee for every mile you drive. And that is before you consider the gas, which at 10mpg, adds up. Yes, if you already own one, you save, but renting mitigates that.
Is there a fuel calculator for RV travel in USA/Canada? will answer the cost of gas piece. The extra gas (10mpg vs. 30mpg) often has a way of costing about as much as the hotel.
Trent over at the TheSimpleDollar.com once did a cost comparison - and when his site is back up, I'll link to it :) In the end, the gas and depreciation was a wash over a hotel.
In the end, its going to cost about the same to stay in a motor home or get hotels. The difference isn't in the cost, but rather the freedom a motor home brings. As a proud and happy RV'er, that alone is worth it.
Alaska in particular has a reputation as being friendly to RVs - the wide open spaces, lack of bridges, etc... actually make driving it fairly common. Still, the Alaska Highway is notoriously long - "miles and miles of miles and miles." Again, if you're looking for cheap, the time savings of a plane should be factored against the drive. If you like the drive (and I do), do the drive - but don't think of it as a magic way to save money.